Dimensional analysis compares the physical dimensions of each term and the final result. Quantities combined by addition must have compatible units, while the answer should carry the dimensions expected for the stated physical variable. A mismatch can reveal an algebraic error, an omitted factor, or an inappropriate equation before numerical values make the result appear plausible.
An order-of-magnitude estimate tests whether a result falls within a physically credible scale, even when the exact calculation is complicated. A value that differs greatly from the expected scale may indicate incorrect parameters, assumptions, or arithmetic. This comparison helps distinguish a meaningful unusual result from an outcome produced by a mistake in the model or derivation.
A limiting-case check examines the model when a relevant parameter becomes very small, very large, or reaches a boundary value. The predicted behavior should remain physically sensible and consistent with the conditions represented by that limit. Unexpected behavior can expose an invalid approximation, an incorrect sign, or a formula that does not apply across the assumed range.
Conservation laws test whether a calculation preserves quantities that the model requires to remain consistent, while boundary conditions test whether the solution matches specified constraints at relevant limits or interfaces. Failure in either check can identify an incorrect assumption or derivation. Agreement does not prove the result, but it increases confidence that the model is internally consistent.
First, inspect the dimensions and units of the equations and final quantity. Next, estimate the expected order of magnitude, examine relevant limiting cases, and compare the result with conservation laws or known boundary conditions. If a discrepancy appears, researchers can revisit algebra, signs, assumptions, or parameters before investing effort in a full rederivation or repeated experiment.
Sanity checks are most useful before accepting a derivation, model prediction, or experimental result as reliable. Applying them early can catch errors while the calculation is still easy to revise, and applying them after obtaining a result can test whether the outcome deserves more detailed analysis. They can therefore reduce unnecessary repetition and guide focused model refinement.
Their specific tests can be applied to mechanics, thermodynamics, electromagnetism, and quantum systems without requiring the same equations in each field. Units, scale, limiting behavior, conservation, and boundary consistency provide general standards for judging results. These checks help researchers separate algebraic or modeling problems from results that are physically meaningful and warrant further investigation.